balancing shifts, ensuring max working time taken into consideration - shift_scheduling_sat.py

[braindeaf]

I wanted to see if there were any opinions on my strategy to balance out shifts in my solver. Forgive me if I paste my Ruby code as an example.

I'm gradually building out my solver into a real world example with real objects user_ids, shifts with hours and various configuration options, real dates, etc At which point it's hard for me to work backwards into Python.

I want to evenly distribute shifts across the period. So that ideally every person gets near enough the same number of shifts. Obviously this won't always be equal, so if num is not an integer we round up.

num = user_ids.count.to_f / dates.count

user_ids.each do |e|
  context.shift_configs.select(&:evenly_distribute).each do |c|
    model.add(model.sum(dates.map { |d| work[[e, c.id, d]] }) <= num.ceil)
    # model.add(model.sum(dates.map { |d| work[[e, c.id, d]] }) >= num.floor)
  end
end

Ideally I'd like to minimize this and say ideally they get num.ceil or num.floor but with a penalty num.ceil + 1, num.floor - 1 etc.

Then we have shifts with their own hours. So here in a given 7 day period we limit the hours for a single staff member to say 48 hours for EU Working Time Directive, and this can be configurable for up to 56 hours if they opt out. But also over the entire period this balances out to more than 40 hours per week (otherwise we may end up with the solver just filling up with too many days off.

user_ids.each do |e|
  # in each 7 day period
  dates[0..-7].each do |d|
    sum = model.sum(context.shift_configs.reject(&:is_rest?).map do |c|
      model.sum((d...d + 7).map { |day| work[[e, c.id, day]] * c.hours })
    end)
    model.add(sum <= users_hours_map[e])
  end

  hours = config.contract_hours * context.num_weeks
  model.add(model.sum(dates.map do |d|
    model.sum(context.shift_configs.reject(&:is_rest?).map do |c|
      work[[e, c.id, d]] * c.hours
    end)
  end) >= hours)
end

Ideally I'd like to minimize this too, less hours is better and balanced hours as much as possible.

Does this all seem reasonable? Any advice?

Many thanks in advance.